H(t)=-4.9t^2+8t+1.5

Solution for H(t)=-4.9t^2+8t+1.5 equation:

(H)=-4.9H^2+8H+1.5

We move all terms to the left:

(H)-(-4.9H^2+8H+1.5)=0

We get rid of parentheses

4.9H^2-8H+H-1.5=0

We add all the numbers together, and all the variables

4.9H^2-7H-1.5=0

a = 4.9; b = -7; c = -1.5;
Δ = b2-4ac
Δ = -72-4·4.9·(-1.5)
Δ = 78.4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{78.4}}{2*4.9}=\frac{7-\sqrt{78.4}}{9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{78.4}}{2*4.9}=\frac{7+\sqrt{78.4}}{9.8}
$